CA Final · Advanced Financial Management · Security Valuation
Under the pure expectations theory of the term structure, the current 1-year spot rate is 5% and the market expects the 1-year rate one year later to be 7%. Under annual compounding, what is the 2-year spot rate, closest to?
Under pure expectations the two-year spot rate is the geometric average of the expected one-year rates. Multiplying 1.05 by 1.07 gives 1.1235, whose square root is about 1.0600 less a hair, so the spot rate is about 5.99%, not the arithmetic 6%.
- A6.00%
- B5.99%Correct
- C7.00%
- D6.50%
Explanation
(1.05 x 1.07) = 1.1235. Square root = 1.05999, so the 2-year spot = 5.99%. The arithmetic mean of 6% ignores compounding, a small but real error, so it is not the exact answer.
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